\contentsline {section}{\numberline {1}问题描述}{1}{section.1}
\contentsline {section}{\numberline {2}理论分析}{1}{section.2}
\contentsline {subsection}{\numberline {2.1}差分格式}{1}{subsection.2.1}
\contentsline {subsection}{\numberline {2.2}迭代方程的推导}{1}{subsection.2.2}
\contentsline {subsubsection}{\numberline {2.2.1}代数方程矩阵化}{1}{subsubsection.2.2.1}
\contentsline {subsubsection}{\numberline {2.2.2}迭代矩阵}{2}{subsubsection.2.2.2}
\contentsline {section}{\numberline {3}程序实现}{3}{section.3}
\contentsline {section}{\numberline {4}运行结果}{3}{section.4}
\contentsline {section}{\numberline {5}优化}{3}{section.5}
\contentsline {subsection}{\numberline {5.1}性能分析}{3}{subsection.5.1}
\contentsline {subsection}{\numberline {5.2}对于矩阵乘法的优化}{4}{subsection.5.2}
\contentsline {subsubsection}{\numberline {5.2.1}思想}{4}{subsubsection.5.2.1}
\contentsline {subsubsection}{\numberline {5.2.2}数学表达}{5}{subsubsection.5.2.2}
\contentsline {subsubsection}{\numberline {5.2.3}程序实现}{5}{subsubsection.5.2.3}
\contentsline {subsubsection}{\numberline {5.2.4}结果验证}{6}{subsubsection.5.2.4}
\contentsline {subsection}{\numberline {5.3}对于迭代的优化}{6}{subsection.5.3}
\contentsline {subsubsection}{\numberline {5.3.1}思想}{6}{subsubsection.5.3.1}
\contentsline {subsubsection}{\numberline {5.3.2}数学描述}{7}{subsubsection.5.3.2}
\contentsline {subsubsection}{\numberline {5.3.3}程序实现}{7}{subsubsection.5.3.3}
\contentsline {subsubsection}{\numberline {5.3.4}结果验证}{7}{subsubsection.5.3.4}
\contentsline {section}{\numberline {6}时间复杂度的探究}{8}{section.6}
\contentsline {subsection}{\numberline {6.1}思想}{8}{subsection.6.1}
\contentsline {subsection}{\numberline {6.2}程序实现与结果}{9}{subsection.6.2}
\contentsline {section}{\numberline {7}结论}{10}{section.7}
\contentsline {section}{\numberline {8}致谢}{10}{section.8}
\contentsline {section}{参考文献}{10}{section.8}
\contentsline {section}{附录: 程序代码}{11}{section*.9}
